Novel Integrity Monitoring for Train Navigation using a GNSS-IMU Bayesian Position Estimator and a Curvature Change Detector

B. Belabbas, A. Grosch

Abstract:	Global Navigation Satellite Systems (GNSS) is a very attractive and popular technique for non-critical navigation. Nearly in every smartphone, a GPS module for navigation is incorporated and more and more cars are equipped with GPS devices. However, GNSS have also the potential to be used for safety of life applications. One of the main challenges for safety of life navigation is to ensure the integrity of the navigation solution, i.e., to guarantee a confidence bound on the solution and to give a timely constrained warning to the user when the deviation to the true solution might exceed an alert limit. For train navigation, the performance of GNSS can be drastically degraded due to local effects like signal shadowing, diffraction, interference, and multipath. The number of unbiased, received ranges drops even below the minimum required number of visible satellites. Consequently, a pure GNSS based position solution without any additional sensors might not be continuously obtained and its accuracy might not meet the requirements necessary for railway applications. The railway environment is more challenging than for other applications such as civil aviation, i.e. we generally encounter a lower visibility of satellites and stronger multipath and interference effects due to an increased number of obstacles as well as a higher potential of intentional and non-intentional interference sources. On the other hand, we do have a very constrained motion, since the trains are bound to move on tracks. If these constrains, i.e. track layout, is available and known at the receiver side, the positioning and localization of the train within this layout can be significantly improved. This is the main key issue for train collision avoidance systems. The most challenging scenarios for these systems is a multiple track change situation where the tracks are dense and are linked with each other by a high number of switches. In this paper, we design and analyze a Bayesian estimator of the train localization within the track layout. Therefore, we take into account all received GNSS raw signals in combination with accumulated inertial measurements such as turn rates and acceleration. In contrast to other studies, our algorithm is not based on a single snapshot solution but it is considering a window of sequential measurements. We show that this sequential algorithm improves the system in terms of accuracy and converging time compared to the snapshot algorithm. Another challenge and innovation of this paper is to estimate the error bounds propagation of the filtered position solution and derive an integrity concept for the fault free nominal error case (only nominal error measurements whose distribution can be bounded by a centered normal one). Furthermore, we also include our curvature change detection algorithm (firstly presented in [1]) in order to even further enhance the system performance. Our integrity approach is based on the derivation of the continuous time diffusion error state equation whose corresponding Fokker Planck equation provides the evolution law of the probability density function [2], [3]. This equation is rewritten taking into account generally accepted GNSS and INS measurement error models. From this filtered error process equation the Zakai equation [4] is derived and the corresponding non-normalized transition density function is determined numerically for some example scenarios. Based on the performance of the curvature change detector, i.e., the probability of wrong detection see [1], the conditional transition density with respect to the detector response is derived for each hypothesis weighted with their corresponding probability. Hyper-surfaces at integrity risk (extension of protection level concept) are derived including their evolution in time for some dynamic scenarios. References: [1] Belabbas, Boubeker et.al., “Curvature Change Detection for Trains using GNSS Coasted with 3DoF IMU”, ENC 2013, Vienna, Austria [2] Grosch, Anja et.al., “Redundant Inertial-Aided GBAS for Civil Aviation”, Navitec 2010, 8.-10. Dez. 2010, Noordwijk, Netherlands. [3] Grosch, Anja et.al., “Parameter Study of Loosely Coupled INS/GNSS Integrity Performance”, ION. PLANS 2012, 24-26 Apr 2012, Myrtle Beach, SC, USA. [4] Xiong, Jie, “An Introduction to Stochastic Filtering Theory”, OUP Oxford, 2008
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	2066 - 2074
Cite this article:	Belabbas, B., Grosch, A., "Novel Integrity Monitoring for Train Navigation using a GNSS-IMU Bayesian Position Estimator and a Curvature Change Detector," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 2066-2074.
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